Reading Response Discussions

Assignment: Find any article using clustered data and describe: the unit of clustering; the hypothesized effects and the level at which the exposure is measured (is it a characteristic of the cluster or the observation within the cluster); and the statistical model used to estimate the effect.  Describe whether there are any other statistical models that might be appropriate and whether they would be preferable (e.g., GEE vs mixed).

Frisvold, D. and Golberstein, E., 2011. School quality and the education–health relationship: Evidence from Blacks in segregated schools. Journal of health economics, 30(6), pp.1232-1245.

Abstract: In this paper, we estimate the effect of school quality on the relationship between schooling and health outcomes using the substantial improvements in the quality of schools attended by black students in the segregated southern states during the mid-1900s as a source of identifying variation. Using data from the National Health Interview Survey, our results suggest that improvements in school quality, measured as the pupil–teacher ratio, average teachers’ wage, and length of the school year, amplify the beneficial effects of education on several measures of health in later life, including self-rated health, smoking, obesity, and mortality.

1. Unit of clustering:
   • Clustering was present at the state level for measures of school quality. [Note: Data was also from the National Health Interview Surveys (NHIS) from 1984 to 2007, which is a multistage probability survey that incorporates clustering.]
2. Hypothesized effects/Exposure measurement level:
   • The exposure of interest was school quality, using state-, race-, and cohort-specific average student-teacher ratio, teacher pay (in 1967 $1,000’s), and average term length for grades K through 12 in public schools to characterize the educational quality averages for each state. Each measure was assigned to an individual based on their years of schooling attended and subsequently aggregated for each cohort in each state leading to weighted averages of 20 years of school quality, which the authors report as an attempt to reduce measurement bias from any specific year. 

   • The authors based their hypothesis on prior arguments that that changes in school quality for black students were conditionally uncorrelated with unobservable variables (e.g. parental support or decisions to move neighborhoods based on district quality) that may be correlated with health outcomes in later life.

3. Statistical model:
   • To estimate the health of individual i born in state s of cohort c at time t, the following equation was used, where Q represents school quality, Y represents years of schooling, Q•Y denotes interaction between school quality and years of school quality, and G is a dummy variable for sex. Fixed effects for birth, birth cohort, and survey year are represented by φ, ξ, and ν. State-specific linear birth cohort time trends are represented by λ_s•t. Random error is denoted by η.
   • Ordinary least squares (OLS) regression used to assess self-rated health (also compared to results from ordered probit), linear probability models were used to assess binary outcomes of smoking, obesity, and disability, and Cox proportional hazard models were used to assess time until mortality. A sandwich estimator was used to account for clustering for all models (heteroskedasticity-robust standard errors clustered on state of birth).
4. Alternative statistical models:
   • The authors aimed to investigate the population-level effects of school quality on health outcomes, indicating that a marginal model such as a GEE (also based on sandwich estimators for variance estimation) would have also been appropriate. The authors could have also employed multilevel modeling, which may have addressed the possible issues of differing sample sizes and effects among states and would allow for the computation of state-specific estimates as well.